Problem: Solve for $x$ : $3x^2 + 21x - 24 = 0$
Explanation: Dividing both sides by $3$ gives: $ x^2 + {7}x {-8} = 0 $ The coefficient on the $x$ term is $7$ and the constant term is $-8$ , so we need to find two numbers that add up to $7$ and multiply to $-8$ The two numbers $-1$ and $8$ satisfy both conditions: $ {-1} + {8} = {7} $ $ {-1} \times {8} = {-8} $ $(x {-1}) (x + {8}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -1) (x + 8) = 0$ $x - 1 = 0$ or $x + 8 = 0$ Thus, $x = 1$ and $x = -8$ are the solutions.